Talk:Pareto efficiency/Archive 1

Removed material
I have removed:


 * The Pareto conjecture hypothesizes that the real world does not contain any Pareto optimizations.

I have not heard of this conjecture. Please cite verifiable sources if you wish to return this sentence. It describes a dark world view indeed! mydogategodshat 00:48, 21 September 2005 (UTC)

Has anyone heard of BitTorrent? Check out http://bittorrent.com to learn about Bram Cohen's creation, which was created as a pareto efficient system.

about pareto efficiency in public finance
I have a homework about pareto efficiency in drug markets. question is "standart public finance theory suggest that patent rights on drugs must be protected because such rights guarantee pareto efficiency.is this true or false.discuss in details" if you can help to me I will be happy thanksssss
 * I think that is covered in WP:WINYH, which is to say Wikipedia is Not Your Homework. --Brokenfixer 06:46, 18 January 2006 (UTC)

Pareto efficient is socialist
This is a socialist hypothesis. It is utterly false in a free market, because there is no way to improve someone without consequences for someone else. Any regulation of the market breaks the definition of the free market that must have unknowable elements, such as new technology or competition for new ways and means--it is how the market become efficient in a free market by competition. The horse-carriage, by example, is no longer popular, but has been used since time immemorial and was replaced by the automobile (every new automobile took away from horse-carriage makers), and this means no economy could be Pareto efficient because the definitions of efficient are inadequate and incomplete. Automobiles dramatically increased the efficiency of Western World societies, and any regulation to prevent changes to make a fake efficient system would be quickly overrun by the other nations willing to throw out Pareto efficient and make the technology advances. Pareto efficient does not explain the modern technology markets and new efficiencies they develop.


 * This isn't a hypothesis, it's a mathematical concept. It has nothing to do with political philosophies, so please keep politics out of this article.


 * In any case, you're contradicting yourself. If there is no way to "improve someone without consequences for someone else" then that's Pareto efficient by definition.


 * Pareto efficiency is defined on a ceteris paribus basis, so whether new technologies emerge in future is irrelevant. 137.222.40.132 17:09, 4 April 2006 (UTC)


 * The condition for pareto inefficiency is not that improvements must have no consequences for somebody else in the absolute sense. There must simply be a net gain from an efficiency change after any "losers" are compensated. Please see below and also in the article for more on this.

Also, new productivity increasing technologies move the [production possibilities frontier] outwards, ie, increase what can be produced. This means that when a new technology becomes available not adopting it creates a pareto inefficiency, because the economy is not producing to its full potential.

Pareto is not socialist. Socialism advocates the redistribution of wealth from top down, person A makes 100 person B and C make 25, everyone therefore should make 50, while this may be communist insert a number slightly higher say 60, 45, 45 to make is socialist. Pareto, from what I learned of it in a class I took involving it, would say this is NOT PARETO OPTIMAL. for it to be pareto optimal, NO ONE GOES DOWN, and at least one person goes up. therefore, to characterize it as socialist is incorrect, because in Socialism the wealthy serve to bring up the poor, which might serve to highlight an overall utility model of society, but not one that guards against any downswing and only goes for the upswing (in an attempt to guard against the situation in Mills' utilitarianism, whereby one person suffering to prop up the rest is acceptable if the average utility or happiness goes up.)

Also, to say that there is no way to improve someone without hurting someone else, shows a great deal of misunderstanding concerning economics and trade. In a situation with perfect information, (the ideal all free markets strive for), or even in the real world without perfect info for everyone, there are many situations where people can make mutually advantageous trades (this is the basis of capitalism as a whole). Trade is not a zero sum game, someone might have one good, and another something else, and to trade half of each stockpile would benefit both parties.

Local nature of optimization
Suggested addition, along the lines of:

A key drawback of Pareto optimality is its localization. As the dictator example illustrates, there can be very many Local optimum points. The Pareto improvement criterion does not even define any Global optimum. Under a reasonable criterion, many Pareto-optimal solutions may be far inferior to the global solution. However, it might be argued that under all reasonable criteria the global optimum will also be Pareto-optimal. Indeed Pareto optimality might be one test of reasonableness.


 * I think I understand what you're trying to say, but I don't think that quite works. While it is important to stress in the article that there are almost always many Pareto optimal solutions, and that depending on the weighting factors (I think that's what you mean by criterion) some will be optimal while others will be suboptimal, you can't say that the number of Pareto optimal points is necessarily a disadvantage. In fact, for people who use Pareto fronts, that's normally considered an advantage. It lets you apply human judgement after seeing a range of solutions, instead of having to choose your weighting factors up front. moink 18:34, 28 Jul 2004 (UTC)

With that in mind, I would emphasize that Pareto efficiency is not really optimality in the ordinary sense, and only provides optimality, albeit robust optimality, in the most limited and local sense. Alex Stark 02:21, 2004 Aug 10 (UTC)


 * Good point. I'll add it. 137.222.40.132 17:14, 4 April 2006 (UTC)

Incorrect affirmation
I removed this affirmation:


 * Also, the attainment of efficiency requires the presence of perfect competition, and is therefore a theoretical goal, not ever likely to be reached in reality.

as I think it is incorrect. In principle, a social planner could set up a system whitch is Pareto efficient. Please discuss before reintroducing AdamSmithee 18:18, 13 May 2006 (UTC) Bold text


 * I concur. Lack of perfect competition does not affect Pareto optimality. Transaction costs are another matter. Haonhien 01:19, 20 September 2006 (UTC)

probably daft question:
is there a typo somewhere in the following? : "If an economic system is Pareto efficient, then it is the case that no individual can be made better off without another being made worse off. It is commonly accepted that outcomes that are not Pareto efficient are to be avoided, and therefore Pareto efficiency is an important criterion for evaluating economic systems and political policies"

or is it a problem in my logic that an outcome in which everyone is made better off is "to be avoided"?


 * A situation in which everyone could be made better off should be avoided, yes -- rather than holding out on everyone, you should go ahead do whatever needs to be done to make them better off.


 * Would you want your boss to say that he could give you a raise but isn't going to (in order to prolong the situation of being able to give you a raise), or would you want him to give you the raise and then tell you that you can't have another one? Sanguinity 20:15, 13 November 2006 (UTC)

Metric Spaces
How do metric spaces play out in the definition of the Pareto set? What is the measure on R^n, and where does it come into effect in defining P(Y)? Sanguinity 20:23, 13 November 2006 (UTC)

In using Pareto sets in engineering, you have some set of inputs, X, that characterize your system (say a rocket or an engine -the set of inputs may be very large). You further have some function with input X and output Y (e.g. different performance characteristics). In order to have one solution dominate another, the criterion vector (output) needs to be a metric space so you can compare them. In the engineering case, the inputs need to be a metric space so you can characterize the differences between solutions. It may be the case that in decision sciences and economics that this criterion may be relaxed such that only Y needs to be a metric space, but I'm not sure if that's the case, and I wasn't able to find any answers in my 20 minute search through papers. If anyone particularly knowledgeable about this comes across this article, please chime in. Similarly, I'm wondering if this article should be broken up into two articles in the future, one that describes the mathematical concept of Pareto efficiency, and another that goes on to the ramifications in economics (and possibly a third into engineering, if we ever get enough written about it... there are a couple commercial and academic software packages that are used quite a bit to find and display Pareto frontiers) Halcyonhazard 18:43, 3 February 2007 (UTC)

New section: Pareto efficiency: a formal representation
The new article section Pareto efficiency now has 2 subsections with the same names as before from the preceding Edit: Pareto efficiency & Pareto efficiency. There is a gain in continuity for grouping the 2 together in formal representation & subject matter. There is also continuity in what comes before them, since earlier sections to do not mention or rely on the new subsections or use a mathematical representation. Those with the necessary math or econ background to follow these 2 sections should not be deterred by such placement. But if they are, there is no reason to make them "eat their spinach." Those without such background are less likely to to be deterred from reading the other sections. The subsections still need to be edited for clarity and context. --Thomasmeeks 21:36, 23 September 2007 (UTC)

Question
I removed this question from Daspranab from the original article, since it belonged here on the talk page instead: "Does Pareto Optimality presumes watertight compartmentalization among individuals? Else, SPO and WPO would not mean the same thing?" Halcyonhazard (talk) 15:40, 21 February 2008 (UTC)

"Formal representation" section: templates for clean-up & references added
Why?
 * 1) There are no page-specific references (or references of any kind) cited for this section.
 * 2) The exposition of the first subsection is opaque & does not correspond to that in the References for the article. There is no verbal translation of the math notation employed.
 * 3) The figure is non-standard in presenting (without comment) Pareto effic. as a minimization rather than maximization condition. --Thomasmeeks 14:58, 14 November 2007 (UTC)


 * Though I'm not an expert in this particular area, I think the choice is quite reasonable in view of mathematics generally and optimization problems in particular. --Ezrakilty 23:46, 30 March 2008 (UTC)

I did some work to clarify the math of the first sub-section, on the Pareto frontier. More could be done. --Ezrakilty 23:46, 30 March 2008 (UTC)

Question about "compensation"
In the article it says: "In the real world ensuring that nobody is disadvantaged by a change aimed at improving economic efficiency may require compensation of one or more parties. For instance, if a change in economic policy dictates that a legally protected monopoly ceases to exist and that market subsequently becomes competitive and more efficient, the monopolist will be made worse off. However, the loss to the monopolist will be more than offset by the gain in efficiency. This means the monopolist can be compensated for its loss while still leaving an efficiency gain to be realized by others in the economy. Thus, the requirement of nobody being made worse off for a gain to others is met."

This makes little sense to me, because in theory the "extra value" that the monopolist is extracting from a market should be equal to the difference in value between the market operating efficiently and the market operating under the monopolist. The extra value that the monopolist gets is the market inefficiency. If you make the market efficient and then try to compensate the monopolist for their loss, the amount that you compensate them should equal any efficiency gains that the market makes, no? Maybe I'm misunderstanding something. —Preceding unsigned comment added by 128.227.137.46 (talk) 19:04, 4 August 2008 (UTC)

weak and Strong Pareto Optimal
I've rephrased the WPO and SPO in the intro,as they (IMHO) were misleading. It seemed to indicate 2 other forms forms of Pareto Optimality, other that restating one and introducing the weaker form. I took as reference |Competitive Equilibrium: Theory and Applications By Bryan Ellickson.

Please correct if need be.

Pbrandao 20:55, 1 October 2007 (UTC)


 * Weak and strong got mixed up, because the source uses the terms "strongly Pareto dominated" and "weakly Pareto dominated". A Pareto optimum is strong, because it is not weakly dominated by any other allocation, whereas a weak Pareto optimum is not strongly dominated by any other allocation. I fixed it anyway. Geometry guy 14:35, 27 October 2007 (UTC)

Right now, it doesn't make sense to me. It says: Strong Pareto Optimum is "a movement from one allocation to another that can make at least one individual better off" and a "Weak Pareto Optimum (WPO) satisfies a less stringent requirement, in which a new allocation is only considered to be a Pareto improvement if it is strictly preferred by all individuals". Surely being strictly preferred by all individuals is a more stringent outcome than being strictly preferred by one individual? Or am I misunderstanding what strictly preferred means? I like this explanation "Pareto efficiency means that no one can be made better off without someone becoming worse off". This is strong pareto efficiency presumably? --Billtubbs 22:38, 1 November 2007 (UTC)

I agree that right now it does not make any sense. I think the weak and strong designations are mixed up. 14 November 2007


 * Distinction between weak and strong too abstract for the lay reader. 69.140.152.55 (talk) 09:39, 22 March 2008 (UTC)

No, I'm confused too. It isn't logical that SPO is a subset of WPO if everyone must strictly prefer the outcome for it to be a WPO and people only have to weakly prefer it for it to be a SPO. If this is the case, an SPO is not a WPO (if something must be strictly preferred then it can't be weakly preferred), but a WPO could be an SPO. Perhaps I'm also misunderstanding what "strictly preferred" means (maybe economists are redefining math terms?). This last comment that the "distinction between weak and strong [is] too abstract for the lay reader" is a bit condescending considering the comments in this section. Surely it's not too abstract. It just looks like someone has gotten things switched around in their definitions. —Preceding unsigned comment added by 216.189.162.121 (talk) 07:22, 8 April 2008 (UTC)


 * The confusion here seems to stem from the difference between a Pareto improvement and a Pareto optimum; a Pareto optimum is a situation in which no further Pareto improvements can be made. However, to qualify as a WPO situation, a new allocation need only be considered a Pareto improvement if it benefits all individuals. In an SPO situation, a new allocation can be considered a Pareto improvement if it benefits all involved or if it benefits at least one individual involved and does not make any individual involved worse off. If there is a possible new allocation strictly preferred by all individuals, the allocation is not Pareto optimal at all; if there is a possible new allocation strictly preferred by at least one and weakly preferred by the rest, the allocation is weak Pareto optimal but not strong Pareto optimal; and if there are no possible new allocations strictly preferred by at least one and weakly preferred by the rest, the situation is strong Pareto optimal and weak Pareto optimal (since there cannot be any new allocations that are strongly preferred by all individuals).
 * 206.180.156.197 (talk) 21:50, 16 May 2008 (UTC)

There doesn't seem to be any reason for the technical tag, so I removed it. The confusion between WPO and SPO seems common, so I will double check that is explained well. But if someone isn't able to wrap his/her head around the fact that an optimum is of a "weaker type" if a more restricted type of improvement isn't possible (but a more general one is), then there's not much we can do short of just saying, "no think about it again". --C S (talk) 19:12, 14 August 2008 (UTC)

Is this supposed to be proof?
"An SPO is a WPO, because at an SPO, we can rule out alternative allocations where no individual loses out, and at least one individual gains. Clearly this is a more restrictive condition than for a WPO, since a WPO still allows other allocations where one individual would gain and nobody else does." Seems like just a repeat of the definition of WPO, rather then a proof to me. How about: "A SPO is a WPO because a situation where an action can benefit all individuals is a situation where one or more individuals are benefited, so an WPO is a state where no more actions can benefit all people at once." —Preceding unsigned comment added by 82.169.240.67 (talk) 00:27, 1 October 2008 (UTC)


 * Well, obviously just before the first period, the following
 * "and these cases where "at least one individual gains" include cases like "all individuals gain"."
 * is implicit. However, I think it ends in a rather sloppy way especially with "nobody else does" which should be "none lose", which is different. I will make the edit.70.81.15.136 (talk) 14:31, 1 October 2008 (UTC)
 * Here, done, but maybe too wordy ? (The "clearly" part is not required, just shows that the converse is not true - WPO is not an SPO.) 70.81.15.136 (talk) 14:38, 1 October 2008 (UTC)

As a solution concept in GT
Would it be useful to put in an equilibrium solution concept infobox into this article? I'm not sure what would go in some of the fields, and maybe it isn't helpful. Smmurphy(Talk) 17:45, 18 March 2007 (UTC) I would like to see more information about Pareto efficiency and Genetic algorithms. Very many of the people visiting this page would be researching multi-objective optimization algorithms, and yet there is not much aimed at them here. I guess it is sometimes a problem when a topic is "owned" by 2 disparate groups. —Preceding unsigned comment added by 118.71.199.230 (talk) 02:59, 5 October 2008 (UTC)

Individuals or criteria?
In the lede and the first section, the notion of Pareto efficiency is defined in terms of the values for "individuals", given a possible "allocation" of goods or such. In the next section (entitled "Formal representation"), the notion is defined in terms of the values of a collection of "criteria", given the choice of a point in "design space". The latter definition is a more abstract generalization. Which is the true definition? --Lambiam 19:23, 12 December 2008 (UTC)

I believe the "informal" explanation of a Pareto efficient situation is wrong
To quote the first paragraph: "Informally, Pareto efficient situations are those in which any change to make any person better off would not make anyone else worse off." Actually, isn't a Pareto efficient situation one in which a change that makes some person better off necessarily makes someone else worse off? —Preceding unsigned comment added by 76.84.46.226 (talk) 16:34, 12 July 2009 (UTC)

To much repetition tag in the first section>
Why is it there in the first place? I don't see what is repetitive about it seems like a very text book introduction to Pareto efficiency 98.71.90.67 (talk) 21:18, 4 December 2009 (UTC)

not Pareto efficient
Could you describe a situation that is not Pareto efficient? Surely if you reallocate resources somebody will allways be made worse off. I am just a beginner at economics can somebody put me right?
 * You are tight if all goods have positive value to all consumers, and all goods are consumed. A simple example of a non-Pareto efficient situation would be one where I want a piece of food, but I just leave it there to rot.  It would be better for me to eat it, while no one is made worse off, since no one else was going to eat it.  Hopefully that helps. Smmurphy(Talk) 17:52, 25 May 2007 (UTC)

Simple examples on what Pareto efficiency really implies in economics can be found here http://www.economics.utoronto.ca/osborne/2x3/tutorial/PEDEX.HTM —Preceding unsigned comment added by 87.119.239.19 (talk) 16:50, 4 September 2010 (UTC)

Definition of an SPO and a WPO: Shouldn't it be the opposite ? (A: No!)
Regarding the opening 3 paragraphs, it seems to me the discussion last year between the definition of an SPO and a WPO was not correctly resolved.

The definition at http://www.answers.com/topic/pareto-efficiency is the exact opposite of what is listed in this wiki, but makes more sense. In my opinion an SPO should require "all" and a WPO should be a single individual, not the reverse as it currently appears to be written. —Preceding unsigned comment added by 152.121.18.98 (talk) 18:37, 29 September 2008 (UTC)


 * Reread the edit I made. I haven't changed the meaning, just clarified. The link you provided makes no sense. Let SPO_OLD be the reverse definition (the one you like), ie SPO_OLD := definition of current WPO, namely where there are no more allocation moves where all would be better and none worse; and WPO_OLD := there are no more allocation moves where at least one would be better but none worse.  How, in this case, could SPO_OLD be a subset of WPO_OLD ? (Inline with the usual "strong vs weak" semantics) Let's say SPO_OLD is a proper subset of WPO_OLD: there are elements -allocations- in WPO_OLD which aren't in SPO_OLD. Take one such element: since it is an WPO_OLD, there is no move where at least one is better off but none worse.  So we just said that there can't be a move where all are better off but none worse either (since these cases are counted in the "at least one" case). This is a contradiction with the "proper subset" affirmation above, but if SPO_OLD is not a proper subset of WPO_OLD but still a subset, then SPO_OLD = WPO_OLD, which is nonsense. 70.81.15.136 (talk) 15:06, 1 October 2008 (UTC)

An additional note to make it easier for you: note that "restrictive" qualifies the definition of optimality or the optimum, not the restrictions or constraints on the set of moves considered. This is part of what I think confuses you: if the set of moves you check for a certain definition of "optimal" (a checklist if you'd like) is big, this definition will be more restrictive than if you consider a smaller checklist. The smaller checklist is more restricted in its scope (constraint relaxation - by removing some constraints required in the definition of optimality in the stronger case) hence the optimality definition is less restrictive. 70.81.15.136 (talk) 15:21, 1 October 2008 (UTC)


 * Is this really an improvement? Just adding more words to dispel a common confusion isn't necessarily better.  Brevity has its virtues.  --C S (talk) 02:27, 2 October 2008 (UTC)
 * I hear you on this. However the part that is more verbose is the
 * "and these cases where "at least one individual gains" include cases like "all individuals gain", the later being the cases considered for a weak optimum"
 * ie: the (evident) proof requested here (I actually mentioned there it may be too verbose for some.) However, I think the (shorter) additions in the other sentence improve the meaning too, as
 * "where one or more (but not all) individuals would gain (and none lose) would still be possible."
 * is more precise and correct, though, like I mentioned, the "clearly" part is not necessarily required. 70.81.15.136 (talk) 05:20, 2 October 2008 (UTC)

Well, I can only offer my opinion as an outsider to the economic community.

Whether or not the answer.com entry is correct, I think it does seem easier for the lay-person to understand for the following reasons: starting at the 2nd paragraph -- 1) it begins with the basic definition "a movement from one allocation to another that can make at least one individual better off, without making any other individual worse off, is called a Pareto improvement". 2) It then essentially lets you know that "Pareto Efficient" and "Pareto Optimal" are the same by stating: "An allocation is Pareto efficient or Pareto optimal when no further Pareto improvements can be made". That way if these terms terms come up again the reader is not confused by the difference. 3) It then avoids going into the complexities and differences between an SPO or WPO until an entirely new paragraph has been started. 4) The next paragraph then begins with the Strong Pareto Optimal, a case where everyone must prefer the new allocation. To the lay-reader, colloquially speaking, any situation where you have to convince EVERYONE is a situation that is more "difficult", "harder", "tougher", "stronger", than a case where you only have to convince one person. So it feels intuitively proper that this is the "strong" case, because if you've got everyone on board, that's a stronger case. 5) It then goes into a WPO, where only one person has to be made better off. An intuitively "weaker", "more frequent" "easier" to achieve case. Since making one person better off is easier than making everyone better off, the "weak" and "strong" terms make sense. 6) (I'm not a fan of the last sentence, but) Stating that an SPO is a sub-set of a WPO also makes sense, in that the rarity of having everyone prefer a new allocation, is smaller, less frequent, less likely, more difficult and makes sense as a "sub-set" of something that only requires one person to prefer the new allocation, which is easy to do. I should note here that it's also easy for non-economists to get confused between "everyone is better off" and "everyone prefers a new allocation", which is what I almost wrote in statement 6). I mention that just because most readers aren't going to know economic history, or make a distinction between normative and positive statements unless they're informed first.

If the entry is being written for both economists and the lay-person, I think it's a little difficult to understand right now. But hey, if you like, we can all do little straw-polls and ask our kids or some people we know who have never heard of Pareto efficiency to read it, and see if they can explain it back to us correctly without any input. I think most people will feel less confused, and be able to parrot back the answers.com entry as stated, more easily than the current entry, even if the wiki entry is technically correct and the other is not. —Preceding unsigned comment added by 68.34.4.171 (talk) 03:18, 3 October 2008 (UTC)

In my opinion, everything in this section except for the first two paragraphs is completely superfluous. This long-winded discussion of different logical formulations of the same point doesn't really add any new information and may even obscure the issue for some readers. I see there's been a discussion about the differences between these two kinds of Pareto optima, and maybe somebody thought he'd clarify the issue by describing it in detail, but this distinction is actually very simple and could be presented much more briefly. I'd suggest deleting most of this section and replacing it with a much shorter definition. Any opinions? RoestiGraben (talk) 10:04, 14 August 2009 (UTC)

I agree - I plan on just removing all discussion of weak vs. strong Pareto optimal. This distinction is not used in economics, the primary application of this concept. If it is used in engineering or something else, it belongs in that subsection, not in the main introductory definition of the concept. Hugetim (talk) 14:13, 16 November 2010 (UTC)

Too technical?
Just one example of a real-world situation where a specified change would increase Pareto efficiency would do wonders to clarify the contents of this article to lay persons. - Gk sa (talk) 16:05, 7 May 2011 (UTC)

Section titles
Are these new section titles, per guideline MOS:HEAD, OK? The old titles are shown in the anchor template. The anchor template may be needed. It repairs links from another article directed to the old section title.


 * ==Efficiency, improvement, and the real world==


 * == Improvement and Microeconomics ==


 * == Weak and strong optimums ==


 * ===A set of choices===


 * === The marginal rate of substitution ===

&mdash; Cp i r al Cpiral  20:49, 30 June 2011 (UTC)

Criticism cleanup
The criticism section is awful. I've seen several complaints about this section in the above discussion, so I'm just gonna go ahead and delete the worst of it.

Let's go through it one by one:

Pareto efficiency does not require an equitable distribution of wealth. An economy in which the wealthy hold the vast majority of resources can be Pareto efficient. This possibility is inherent in the definition of Pareto efficiency; by requiring that an allocation leave no participant worse off, Pareto efficiency tends to favor outcomes that do not depart radically from the status quo. It is also argued that Pareto efficiency does not always result in the socially optimal, in terms of efficiency and equity, distribution of resources; thus, necessitating redistribution programs.[1]

Pareto efficiency refers to markets. In a communist utopia, a Pareto efficiency won't exist (well, it will, but that won't concern the communist New Class). This isn't a criticism of Pareto efficiency, this is a criticism of capitalism. It doesn't belong here. (I'd actually contend that a lack of Pareto efficiency is nearly chief among the deficiencies of communism, but I digress.)

Nobel prize winning economist Amartya Sen has elaborated the mathematical basis for this criticism, pointing out that under relatively plausible starting conditions, systems of social choice will converge to Pareto efficient, but inequitable, distributions.[2] A simple example is the distribution of a pie among three people who each want as much of the pie as they can get. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients is left worse off than before (when none had pie); there are many other such distributions (any where the entire pie is distributed). An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded, as welfare can be increased without reducing the welfare of any individual (e.g. just give the quarter pie to someone). The origin of the pie is conceived as immaterial in these examples, i.e. the pie was "free." In such cases, in which a "windfall" that none of the potential distributees actually produced is to be allocated (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation.

This "free" pie thing is incredibly contrived—land doesn't come from nowhere, inherited wealth is doled out according to the wishes of the deceased, and broadcast spectrums are typically auctioned off to the highest bidder by the FCC or similar agency (basically, who can best capitalize it is willing to pay the most for it). There's not a single a real-world example I can immediately think of that can fit this, and it's simply to awkward to be a serious criticism. For some unlikely edge case Pareto efficiency doesn't apply? Please.

This second paragraph might belong somewhere else, but it's not really criticism of Pareto efficiency, but, like the first example, a case where Pareto efficiency isn't the best option. You wouldn't criticize a car because it can't drive underwater, why would you criticize Pareto efficiency for something it was never intended to solve?

The third paragraph I'm leaving, despite that it appears to be original research. While the issue of local maxima may be small or negligible here, this is potentially the first legitimate criticism in this section.

The last paragraph may be the worst of all:

"Despite its drawbacks (or perhaps precisely because of these drawbacks),"

This is just bad writing.

"Pareto-efficient improvements to real-world economic systems are extremely rare, and considered 'the holy grail' of economic improvements."

This is absurd—Pareto-efficient improvements are the basis of entrepreneurism, and incredibly common. Someone creates a new product, or more efficiently produces an existing product. This creates a boom of wealth for everyone: entrepreneurs gain a large amount of wealth in the form of money, while customers collectively gain a large amount of wealth in product. This happens every single day.

"They can be thought of as 'free money' in some sense- someone's lot is improved without taking anything from anyone else."

No, it can't be—there's no such thing as a free lunch. Pareto efficiency improvements happen when individuals work hard and that effort pays off for them and society. The economy isn't a zero-sum game, and regularly expands and contracts. None of this is free though, it's earned.

"One of the other benefits of such improvements is that they do not require the social planner to define a 'social welfare function,' a (necessarily arbitrary) weighting system which reflects the priorities given to the welfare of each individual in society."

This is irrelevent even if the rest of the paragraph weren't being deleted.

If you feel you can clean these up enough to be re-included, be my guest. For now, they're just gonna have to sit it out in Wikipedia's history.--71.234.44.178 (talk) 05:34, 11 May 2008 (UTC)


 * I want to second your editing of this section and agree wholeheartedly with your arguments. I had considered performing a similar edit, but because I'm not as trained in the softer side of econ and politics (my research is in computer science and have done work with game theory and mechanism design in resource allocation), I just wasn't sure if these views were held in certain political science or econ circles. Halcyonhazard (talk) 04:08, 12 May 2008 (UTC)


 * Although I disagree with some of your (71.234.44.178) criticisms (the pie metaphor was a useful way to visualize the concept), I agree that the section was problematic and you may have been right to remove it. After all, "Pareto efficiency" is just a formal criterion one can use to evaluate a situation, and not really a normative ideal (or so I think; I'm not an economist), so a section of social "Criticisms" seemed out of place. Indeed, the section was too narrowly focused on one interpretation or use of Pareto efficiency in economics, and ignored other possible uses, such as in game theory. Ezrakilty (talk) 19:43, 12 May 2008 (UTC)

I deleted another paragraph from the criticism section, as it was specious. The text read:

"For instance, allocating all the world's resources to one person and leaving the rest to starve is Pareto-optimal, as any re-allocation would take from the one with everything; allocating resources equally, but throwing a few in the ocean is not Pareto-optimal, as it wastes some resources. However, this latter (non-Pareto-optimal) allocation is widely preferred to the former (Pareto-optimal). Thus, when comparing two allocations, the fact that only one is Pareto-optimal is not in itself sufficient reason (or, for some, much reason at all) to prefer the Pareto-optimal one."

The time scale of allocation is ignored here. Either (1) all goods are distributed in some fashion prior to the author's allocations, or (2) the author has a new world in which s/he is attempting to allocate the goods. If (1), reallocation to give one person all the goods is itself Pareto-inefficient, so it is irrelevant that reallocation from that point is Pareto-inefficient. If (2), once the resources are allocated, either situation is Pareto-efficient. Throwing resources in the ocean at the moment of allocation simply diminishes the resource volume; they are not recoverable, so the system is (sans wasted resources) Pareto-efficient.

A Pareto-inefficient allocation would have a stockpile of non-perishable resources. That is, the requirement of Pareto inefficiency is the ability to redistribute extant resources without detriment to any individual.

So why didn't I just change "ocean" to "stockpile"? I didn't think of it. And, as noted above, Pareto efficiency is descriptive, not normative. The only thing to criticize is misunderstanding of the term or willful misuse of the fact that "efficiency" is in the name.Lmdav2 (talk) 03:47, 10 March 2009 (UTC)

Would recommend adding back in some form of "criticism" section. Perhaps a cite to Moshe Adler's "Economics for the Rest of Us" would be in order there. — Preceding unsigned comment added by 67.51.122.18 (talk) 22:56, 14 February 2012 (UTC)


 * I agree that Pareto efficiency should be considered a descriptive concept, thus "criticism" may simply be POV. The present text is helpful, however, in explaining that Pareto optimality does not imply equitability and that it does not imply unimprovability-by-some-measure. Ezrakilty (talk) 19:01, 10 March 2009 (UTC)

Dictator analogy, pie example
I have removed the bit about a dictator being an undesirable Pareto efficiency. Pareto efficiency deals with markets, something definitionally unapplicable to dictatorships. This is also applicable to the silly bit above about it being somehow "socialist." Pareto efficiency is not about the winners winning more than the losers lose. Rather, it says that in a free market losers' loss will be negated by some other market compensation. 68.98.158.194


 * I reintroduced the example as it is very easy to understand, being somewhat extreme. If you don't like the dictator thing, maybe it would be better to reword the example than to remove it AdamSmithee 18:18, 13 May 2006 (UTC)

I removed the dictator example again but not because of any political preference. Unfortunately it was based on a common misunderstanding of the "better off with no worse off" necessary condition for Pareto efficiency. Acheivement of Pareto efficiency only creates the potential for this condition, but does not necessarily distribute wealth like this in practice. This is acheived in practice by compensation to those hurt by the policy change, with the efficiency gain outweighing the amount of compensation required and resulting a net gain. Thus, the case that a dictatorship is always a Pareto efficient economy is not correct, if a re-organisation can result in a net economic gain after the dictator has been compensated for his/her loss. Please see the other part of my edit in the begining section for changes explaining this.

I'm not entirely sure of the strict relevance of the pie example to the concept of Pareto efficincy either. It appears to prove that Pareto efficiency can exist alongside inequity due to social choice, but doesn't prove that Pareto efficiency drives inequity. We need a citation by Sen to prove that he was directing his critisism towards Pareto efficiency and that his ideas have not been extrapolated by others here.


 * I have serious doubts about the pie example as well or the need to invoke magic falling pies produced by no-one. MaxEnt 08:14, 18 July 2006 (UTC)


 * I don't consider the fact the pie falls out of the sky is a problem. Some real-life situations are very similar: Every year, Alaska gets a tax surplus which it must divide. That's a pie from the sky. They've been dividing it equally among residents, but obviously that's not the only way to divide. Technological advances that create new resources, such as new radio frequencies, are also similar. As an example, the "falling out of the sky" aspect of it is not a big problem to me.
 * My problem as to do with relating this pie example to Amartya Sen's work. I am (or rather, was) familiar with Sen's Paretian liberal paradox, but I have some difficulty relating that paradox to the pie ending up divided among 2 of the 3 players. Maybe some explanations would help. Haonhien 01:17, 20 September 2006 (UTC)

I don't understand the purpose of the criticism section at all. It seems to do little more than point out that there is inequity in the world, and contributes little to the article. It reads more like a political statement than an attempt to add to the understanding of Pareto optimality. Maybe this section should be rewritten in a more neutral, abstract manner using strictly mathematical examples to show that there are multiple Pareto optimal solutions, not all of which are "fair". If there are no objections, I'll start putting together some examples.

192.165.213.18 21:53, 26 March 2007 (UTC) Yeh, pareto efficiency is just communist maths, and hence is not true even if the formula are true. All you need is the bible and a gun. —Preceding unsigned comment added by 118.71.199.230 (talk) 02:36, 5 October 2008 (UTC)

I have doubts if Pareto efficiency is correctly interpreted... Let us consider a simple example... Imagine that a CEO discovered that one of his employees, call him Jimmy, is negligent and produces waste. So, following a common sense he would fire Jimmy and hire more productive Tommy. But this decision will be Pareto inefficient, as the result of this measure is making Jimmy worse off. So under the Pareto efficiency principle we are not allowed to make compromising decisions when we make better for someone doing worse for somebody else. But if so, then Pareto efficiency contradicts to the maximum productivity principle. This rule also contradict to the following definition of Pareto efficiency: "The Pareto frontier is particularly useful in engineering: by restricting attention to the set of choices that are Pareto-efficient, a designer can make tradeoffs within this set, rather than considering the full range of every parameter." What is meant here with the term "tradeoffs". Maybe I misunderstand something... Why it is often asserted that Pareto optimality should be a decision rule for any of the economic problems?" In this article we read "It is commonly accepted that outcomes that are not Pareto efficient are to be avoided, and therefore Pareto efficiency is an important criterion for evaluating economic systems and public policies." To my mind Pareto efficiency cannot be a final criteria of effectiveness. It only says whether society is in the state of underuse of its potential or the opportunities to increase someone's well-being without making worse for somebody else are fully exploited.  I have found an interesting paper on the issue http://www.analyse-und-kritik.net/en/1980-2/AK_Backhaus_1980.pdf  Also this book on page 2 provides some insights http://books.google.ru/books?id=nIrnw4tQ7qEC&printsec=frontcover&dq=%22welfare+economics%22&source=bl&ots=u34UljUC-6&sig=HeY0kHvBLaz0XpcMvz4TGGGbgfI&hl=ru&ei=ZDuBTOWzHuiTOI3SxY4O&sa=X&oi=book_result&ct=result&resnum=8&ved=0CD8Q6AEwBzge#v=onepage&q&f=false In the above reference the author states that it's efficiency in a narrow sense of exhausting the gains from trade. I believe it should be cleared that Pareto efficiency is a limited notion based on some restrictive assumptions. And that it doesn't follow that making some people better off and other people worse off (redistribution of income) can be an effective policy it the benefits for gainers outweigh the losses for some people. For example,in the case of posing restrictions on monopolies. —Preceding unsigned comment added by 87.119.233.131 (talk) 16:18, 3 September 2010 (UTC)


 * To address your CEO example, employing Jimmy and having Tommy unemployed would not be Pareto efficient because a Pareto improvement is possible: hire Tommy but continue paying Jimmy his old salary. (To be precise about it, we'd need more detail, but that's the basic idea.) Otherwise, as the current article states in the intro, "Pareto efficiency is a minimal notion of efficiency and does not necessarily result in a socially desirable distribution of resources: it makes no statement about equality, or the overall well-being of a society." Hugetim (talk) 19:31, 20 June 2012 (UTC)

Voting system criteria
This article is in Category:Voting system criteria, but it doesn't mention any form of the words vote, elect, or candidate. Someone might want to mention the voting connection in the article, or just remove it from the category, whichever is more appropriate. - dcljr (talk) 22:53, 8 May 2011 (UTC)
 * The same can be said about Bayesian efficiency, BTW. - dcljr (talk) 22:56, 8 May 2011 (UTC)
 * Pareto efficiency is also not mentioned at . I believe it is not commonly used as a voting system criteria because Arrow's impossibility theorem proves that achieving it requires giving up some more basic property of a desirable voting system. So I favor removing it from this category, but I am not sure about this. Hugetim (talk) 20:10, 26 June 2012 (UTC)

Work, where the term was introduced
Hello!

It'll be very usefull to add two things to the article (I don't know the answers here, that's why I'm not adding them myself):

+100 to anyone who know the answers and will add them to the article --Zarutskij Svyatoslav (talk) 16:23, 30 September 2012 (UTC)
 * 1) In what non-Pareto work the term "Pareto efficiency" was introduced?
 * 2) In what work Pareto himself used, what was later called "Pareto efficiency"?


 * Of possible interest: In his influential A Theory of Justice John Rawls relies heavily on Pareto optimality. (Or as he calls it, the principle of efficiency.) In the note on p. 66 he says:


 * "There are expositions of this principle in most any work on price theory or social choice. A perspicuous account is found in T. C. Koopmans, Three Essays on the State of Economic Science ..., pp 41-66. See also A. K. Sen, Collective Choice and Social Welfare ..., pp. 21f. ... The principle of efficiency was introduced by Vilfredo Pareto in his Manuel d'economie politique (Paris, 1909) ch. VI, §53, and the appendix, §89. A translation of the relevant passages can be found in A. N. Page, Utility Theory: A Book of Readings ..., pp. 38f. The related concept of indifference curves goes back to F. Y. Edgeworth, Mathematical Psychics (London, 1888), pp. 20-29; also in Page, pp. 160-167."


 * Buchanan and Tullock, in their classic The Calculus of Consent, also rely heavily on Pareto optimality, but (hiss, boo) cite no sources. ~ J. Johnson (JJ) (talk) 20:54, 22 December 2012 (UTC)

Merge with multi-criterion optimization?
I am surprised that so little math is used in this article. Consequently, the definition of Pareto optimal solutions is informal and rather naive. The last section on Pareto optimalizty in engineering does introduce more math but again in an unsatisfactory way. The problem might be that I am an engineer but the authors of this article seem to be economists and philosophers.

I believe that Pareto optimality should be explained in terms of multi-criterion (or multi-objective) optimization and partially ordered sets. It's very simple: Pareto optimal points are minimal points of the vector-valued objective function with respect to the product (partial) ordering. See e.g. the book [Boyd-Vanderberghe: Convex Optimization]. The rest of the article should be treated as the historical background to this definition.

In any case, the article should be merged with (or at least it should cite at the very beginning) the article on multi-objective optimization. --90.180.171.120 (talk) 20:11, 19 December 2012 (UTC)


 * As you say, you're an engineer. In economic theory and even moral philosophy Pareto optimality seems to have been enshrined as not just a form of optimization, but as the preferred, even exclusive, form. In this context it is highly notable (see previous section) in itself, even if debased.  I suspect a two-level approach is needed, reflecting different derivation and use in engineering vis-a-vis philosophy. ~ J. Johnson (JJ) (talk) 21:18, 22 December 2012 (UTC)

Example in the introduction
In my opinion the example is not very good. While (10,10) is Pareto optimal, so are (9,11) and (11,9). As long as it is (n, 20-n) it's Pareto optimal: you cannot make one side better without making the other worse. Unless of course A and B always get the same amount of X. But then (9,11) and (11,9) couldn't exist. 168.87.60.62 (talk) 15:37, 9 April 2013 (UTC)

Took out some unneccessary qualifiers from the Criticisms section
It seemed to be POV in the current wording, using words like "widely criticized" and "strongly" where they were not warranted

Akshayaj 21:01, 12 July 2007 (UTC)

MISTAKE: In the criticism, the fact that one person can have no slice and someone else has 2 slice being pareto optimal assumes a linear utility function (i.e. that marginal utility doesn't decrease with wealth). Otherwise, the equitable allocation would be the best as everyone would have the highest possible utility for their slice. Hence this would be pareto optimal and not the inequitable solution. --203.158.33.213 06:26, 19 August 2006 (UTC)
 * So does the example in the introduction. Without knowledge of the utility function you can not claim, the going from (10,10) to (11,9) is not an improvement. --91.45.251.135 (talk) 12:37, 11 July 2013 (UTC)

I agree that a discussion of the different utility functions is badly needed in the article. Rather than to talk about a pie an example with fruit could be used: a boy got an apple and a girl received a banana from their respective fathers. However, both the two children preferred the other child's fruit compared with its own. Therefore, by changing fruits there would be a Pareto efficient solution. To a large, extent different utility functions are a reason why trade occur. Also, it might be a good idea to mention the common assumption that the extra utility from each extra piece of good decreases with each piece. In other words the first apple tastes better than the second and the second tastes better than the third etc. This influences the utility functions of all people for all sorts of goods and services. With different utility functions and different amounts of goods and services with different individuals it's clear that the total utility will increase if the goods and services are redistributed. This is the basic idea behind Pareto efficiency. In history there have been different ideas for how to accomplish this effect. The idea of (utopian) communism was that people would voluntarily hand over goods and services to people with great needs. Even without considering that people are too egoistic for this to work out, in a in world with many different kinds of goods and services and many individuals an information problem occur. How to collect and distribute information about the individuals’ utility functions, the number of different goods available, etc? In a market economy this is no problem since the relative utility functions of the population and the relative scarcity of goods in reflected in the price level for all goods and services. At the very beginning of the 20th century (before the Russian revolution) there was a debate between economists whether an adequate allocation of resources could be achieved in communism, since information about the relative scarcity was not given. Perhaps I should not get into depth on the different arguments in this extremely interesting discussion. Anyway critics of communism foresaw basically problems, which later occurred in economy of the Soviet Union. Strangely enough it's generally considered that the debate was won by the proponents of communism. The reason is that they came up with the concept that there should be artificial trading giving sort of market prices in an economy without personal ownership. In the Soviet Union the main sort of allocation was through administrative action. Therefore after a while changes in individuals' and companies' utility functions as well as relative scarcity of goods and services were no longer reflected in the prices of goods and services. This is one of the main reasons why it was so difficult for the Soviet Union to achieve Pareto efficient solutions. In short, Pareto efficient solutions can be reached in different ways, but in a system with flexible prices such solutions are easiest to attain through trade. Somehow these ideas should be added to the article in one way or the other.Smallchanges 18:34, 9 October 2006 (UTC)
 * This is facinating. Any references for further reading about this would be appreciated. 74.210.53.170 03:06, 16 June 2007 (UTC)

"In a market economy this is no problem since the relative utility functions of the population and the relative scarcity of goods in reflected in the price level for all goods and services."
 * Only if you define "relative utility functions" this way. Than of course it is trivially true, but does not stand a reality test, unless you consider it optimal, that a starving person has no food while another one has an abundance of it, only because the starving person has not money and therefore no influence on prices. --91.45.251.135 (talk) 12:50, 11 July 2013 (UTC)

I don't understand why it is considered better for someone to benefit at another's expense, rather than benefiting at no one's expense. Is it based on the assumption that if it is possible(to benefit at no one's expense), then resources were not being used properly? If this is true, it still seems that it would be desirable, as long as everyone was content, since no one would need to be made less content for others to become more content.
 * That basically is the idea behind Pareto efficiency. If something is not pareto efficient, then resources are not being used properly, since someone can be made better off without making any one else worse off. Is the page somehow confusing that? Jrincayc 14:49, 23 Nov 2003 (UTC)

"A change that can make at least one individual better off, without making any other individual worse off is called a pareto improvement."

"If an economic system is not Pareto efficient, then it is the case that some individual can be made better off without anyone being made worse off.

Aren't these contradictory? If the change makes someone better off without making anyone else worse off, it is an improvement. However, if the system is not pareto efficient, then you can make someone better off without anyone else being made worse off. So it's an improvement to make the system less pareto-efficient?
 * It is confusing at first read because the first sentence refers to an economic activity (change) whereas the second refers to an economic system. Simply put, they just say that an economic system will not be perfectly Pareto effecient if there are opportunities to engage in economic activities that contribute to Pareto efficiency. The second statement could be reformulated tautologically to say "If an economic system is not Pareto efficient, then a Pareto improvement would be possible. mydogategodshat 20:19, 7 May 2004 (UTC)

Regarding the interpretation of the graph
At one point, the writer says, "...Any point on the frontier curve is Pareto efficient...". The question is why? This needs to be explained clearly. It does not appear that any point on the frontier curve is Pareto efficient. What do you mean by the frontier curve? The blue curve? Only the arc whose endpoints are created by the lines perpendicular to the co-ordinate axes subtended from the point A and extended to meet the said curve at the respective endpoints. — Preceding unsigned comment added by Bkpsusmitaa (talk • contribs) 05:34, 12 January 2013 (UTC)
 * Yes, the blue curve represents the production–possibility frontier (and is usually represented by an outward-bulging line, though other shapes are possible). Any point within the curve represents productive inefficiency or underutilization of certain inputs. In this very simplified example, any point along the curve is Pareto efficient and any movement along the line would not be able to result in Pareto improvement because at least one individual would be made worse off by the change. I feel the article and caption for the graph do an adequate job of explaining this. --Everlong (talk) 18:54, 12 January 2013 (UTC)

I find the graph and the description of the graph very confusing. Colouring part of the production-possibility frontier, which is also the Pareto-Efficient Frontier, red while the rest of it is blue, combined with the arrows, gives the impression given is that the red bit is the Pareto-Efficient Frontier, while the Blue Part (and points B and C, at least) are not Pareto Optimal/Pareto Efficient. But they are. And what is point X doing there? Presumably it's not attainable, but it's not even referenced in the description. As a minimum, I think the graph should be redrawn to remove the arrows, the whole Pareto-Efficient Frontier should same colour and point X should either be removed or referred to as unattainable/infeasible. Further, either labels or the text need to make it crystal clear that points B, E, D, F, and C are all pareto optimal. I have also commented in the section below, agreeing that the description of the graph is wrong (or at least, so clear as to be misleading). — Njr (talk • contribs) 14:00, 19 February 2014 (UTC)

Description of graph wrong?
"Moving to point C from point A, is not a Pareto improvement, as less butter is produced. Likewise, moving to point B from point A is not a Pareto improvement, as fewer guns are produced."

Shouldn't it be the other way round? From A to C: less guns are produced (and more butter). From A to B: less butter (but more guns) — Preceding unsigned comment added by 131.130.14.186 (talk) 12:37, 22 April 2013 (UTC)


 * Moving from A to C or from A to B is irrelevant, because A is not in the Pareto frontier - moves like A->D exist that improve both axis. The moment one possible improvement exists from the current point, it's not Pareto efficient no matter what other movements can be made from it. Diego (talk) 21:53, 22 April 2013 (UTC)


 * You're right. The description is wrong. And congratz to Diego for missing the point by a few light-years. ;) 168.87.60.62 (talk) 14:41, 23 April 2013 (UTC)


 * The description and Diego are correct. Simply put you can only move in the supply space where guns increases for no reduction in butter, where butter increases for no reduction in guns or where both butter and guns increase. When you move, neither the butter lover or gun lover can be worse off for the move to be a Pareto improvement. To be efficient the point must be on the frontier. To move from A to the frontier, a Pareto improvement can only occur in the arc AEF 80.231.29.105 (talk) 13:48, 1 August 2013 (UTC)

I think the graph itself is wrong. I agree that moving from A to either B or C is not a Pareto improvement, but that doesn't mean that B and C are not efficient. By definition, "Pareto efficiency, or Pareto optimality, is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off." It seems to me that B and C both fit this criteria. In other words, the set of Pareto efficiencies do not depend on the current location (A). The whole curve is Pareto efficient. Also, "X" should be taken out, since it is not a possible state and is not mentioned in the description.132.200.32.34 (talk) 21:03, 6 December 2013 (UTC)

I don't like the graph or the explanation (see above, re. the graph. The text describing the graph is unnecessarily convoluted, and fullnot helped by the sentence "Suppose that there are two agents in an economy, guns and one that only values butter." I suppose that's supposed to say "one that only values guns", rather than just guns.

It seems as if the reason the section from E to F has been made red is that if current production is at point A (not Pareto Optimal), moving to B or C would not be Pareto improvements. That's true, but the cost of including it here is to make explanation of the Pareto Efficient Frontier very hard to follow. Personally, I don't think this is an important enough point to mess up the graph. If people think it's and important point to make, I think it should get a second graph, rather than messing up the one showing Pareto Efficiency.

I'm very tempted to replace the graph with a much simpler one and to rewrite the explanation

Njr (talk) 14:06, 19 February 2014 (UTC)


 * please fix if you can. Although B and C are not Pareto improvements over A, they are Pareto efficient. -Hugetim (talk) 15:26, 19 February 2014 (UTC)

Somewhat shocking ...
... or would be. Apparent random loss of content and degradation of an important article due likely to some citoyen venting opinion by destroying valuable content. At least that's what I gather from no discussion found above. Have restored with some further maintenance. Lycurgus (talk) 18:16, 13 September 2014 (UTC)

Overhaul explanation
I've just made a major overhaul of the article in a series of edits. I expect that this might upset some people who put time into writing the parts I removed, so I wanted to add a brief explanation here and invite discussion. As an economics teacher, this article has bothered me for a long time because it has been overloaded with irrelevant technical details and contradictory explanations, making the topic appear unapproachable and incomprehensible. I have spent some time on this revision and made a good faith effort to retain all of the substantive content, while correcting some mistakes and removing repetitive and overly verbose explanations.

(Minor comments: If anyone knows of an application of "weak Pareto optimum," a citation would be helpful - I am unaware of any use of this concept in economics but retained it out of deference to previous contributors. I would actually be in favor of removing it completely. Also, a reference to an engineering source on Pareto efficiency would allow us to remove that banner.) Hugetim (talk) 19:13, 20 June 2012 (UTC)


 * Not sure what your edits contributed to the state I found this in but apparently the weak &sect; was added after that. In any case this is a really important topic in applied mathematics, namely game theory, where it's ubiquitous and fundamental. Actually think most of what I've restored was prior to your edits so dunno but looked hacked, vandalized and maybe in a roundabout way, semi-intentional way it was but think major part was before your edits. Lycurgus (talk) 18:30, 13 September 2014 (UTC)

What is a "Pareto Efficient Frontier"?
The lower of the two graphs shows the Pareto Frontier that is explained in the text. The upper graph shows something else and says it is a Pareto Efficient Frontier. It is apparently not a Pareto Frontier (which is explained in the text and in the lower graph) because the point N would be Pareto efficient. So I deduce that "Pareto Efficient Frontier" and "Pareto Frontier" are two different concepts. However, the only mention of "Pareto Efficient Frontier" is in the upper graph. This is extremely confusing and the upper graph doesn't seem to illustrate anything shown in the text. What's going on here? 130.233.158.198 (talk) 10:51, 14 August 2015 (UTC)

Dr. Kebede's comment on this article
Dr. Kebede has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"very good article"

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Kebede has published scholarly research which seems to be relevant to this Wikipedia article:


 * Reference : Bereket Kebede & Marcela Tarazona & Alistair Munro & Arjan Verschoor, 2011. "Intra-household efficiency; An experimental study from Ethiopia," CSAE Working Paper Series 2011-01, Centre for the Study of African Economies, University of Oxford.

ExpertIdeasBot (talk) 09:16, 16 June 2016 (UTC)

Criticism section could use rewording
The criticisms of Pareto efficiency appear to be directed at specific applications rather than at the Pareto efficiency itself. It may be helpful to remove these criticisms, or to clarify that the criticisms are confined to specific social and economic applications. As it stands, the criticism section has no relevance to engineering or computer science applications, and this is not clarified in the section itself. — Preceding unsigned comment added by 66.46.99.242 (talk) 19:45, 8 June 2016 (UTC)

"It would be invalid to treat Pareto efficiency as equivalent to societal optimization, since the latter is a normative concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution."

Which is invalid because an unequal distribution of resources causes a thinner market and therefore a loss of economy of scale. In other words, a fair distribution of the factors of production produces Pareto efficiency which is also optimal from an equality POV..

http://markwadsworth.blogspot.co.uk/2015/09/deadweight-loss-of-excess-inequality.html — Preceding unsigned comment added by 77.102.67.217 (talk) 01:24, 5 January 2017 (UTC)

Pareto frontier
The material on the Pareto frontier is contained in the use in engineering section. The concept of a Pareto frontier is also widely used in economics. The concept should therefore be accorded a general treatment, followed by examples from economics and from engineering in their corresponding (sub)sections. This is a bit outside my field, so I will leave any improvements to someone better qualified than me. Best wishes. RobbieIanMorrison (talk) 14:03, 13 January 2017 (UTC)

Pareto Efficiency
Confused about definition:


 * "Pareto efficiency or Pareto optimality is a state of allocation of resources from which it is impossible to *reallocate* so as to make any one individual or preference criterion better off without making at least one individual or preference criterion worse off"

Define reallocate. What does it mean? Move *one* resource from one to another, or a completely new allocation? Has a big impact on the meaning. — Preceding unsigned comment added by 136.186.248.1 (talk) 03:36, 8 March 2017 (UTC)